# Calculating Trajectory of a Plane Flying at 100m/s

• qubert
In summary, the conversation discusses how to plot the trajectory of a bomb dropped from a plane flying at a speed of 100m/s and a height of 18m above water. The next part of the problem asks for the number of bounces and horizontal distance the bomb will travel without bouncing over, with the constraint that the resultant speed must be between 5 and 6m/s. The conversation suggests using equations to calculate the vertical and horizontal velocities at each bounce, with the mass of the object canceling out. The coefficient of restitution is also mentioned as a possible factor to consider.
qubert
Question is:
plane flies at a speed of 100m/s at a height of 18m above water
plot the trajectory from release to first impact point, in intervals of 0.2m

managed this and have plotted the trajectory, with relevant velocities and resultant but the next part asks:

"At each bounce the vertical and horizontal velocity is reduced by a factor of 0.696, if the resultant speed has to be between 5 and 6m/s determine the number of bounces and horizontal distance the bomb requires without bouncing over."

how would one rearrange the equations finding the first trajectory without knowing the height the second bounce starts from?

i thought maybe by using a quadratic and pythagoras:

(100x0.696B)^2+(18.78x0.696B)^2=5.5^2 where b is the number of bounces, 100 and 18.78 are the horizontal and vertical velocities on the first drop

is this anywhere near correct?

thanks

Last edited:
Firstly just consider the vertical direction.
Assume all the potential energy turns into kinetic at the ground.
Calculate the potential energy at the start and the kinetic energy at impact to get the vertical velocity at impact
Then use the new velocity to get the kinetic energy that it starts back up with.
Use this to get the potential energy and so the height of the next bounce.

Once you have the height and so the time for each bounce you can also get the horizontal velocity for each bounce in the same way.

I woudl probably do this a line at a time eg on a spreadsheet rather than trying to write an analytical eqaution for the end result.

is it possible to work out the potential energy without the mass of the object? would there be another way to work out the height of the next bounce?

The mass is in the potential energy and the kinetic energy so it cancels out.
If the only change is in the velocity then you can only work it out with kinetic energy, of course you can write the an equation for the height of the next bounce but that is just using ke/pe anyway

so pe=176.4j before being dropped and ke=176.4j at impact, how would it be rearranged to find out the new velocity? (ive never used these formulae before so sorry if I am slow) is the co efficient of restitution used here at all? thanks

Last edited:
ke = 1/2 mv^2 so V = sqrt( 2 ke / m )
Then the V immediately after the bounce is 0.696V or you can use the equation to calcualte what the change in KE would be directly without workign out the speed.

sorry I am still not following, would i be able to send you the excel spreadsheet i have so far so you can take a look at what I've done? thanks

## 1. How is the trajectory of a plane calculated?

The trajectory of a plane can be calculated using the laws of physics, specifically the principles of motion and forces. The initial velocity, acceleration, and air resistance are all factors in calculating the trajectory of a plane flying at 100m/s.

## 2. Can the trajectory of a plane change during flight?

Yes, the trajectory of a plane can change during flight due to various factors such as wind speed and direction, air turbulence, and changes in engine power. In addition, pilots can adjust the trajectory of the plane by making course corrections.

## 3. How does air resistance affect the trajectory of a plane?

Air resistance, also known as drag, can have a significant impact on the trajectory of a plane. As the plane moves through the air, it experiences resistance which can slow down its speed and change its direction. This is why planes are designed to be aerodynamic to reduce air resistance and maintain a stable trajectory.

## 4. Is the trajectory of a plane affected by its weight and size?

Yes, the weight and size of a plane can affect its trajectory. The heavier and larger the plane, the more force is needed to keep it in motion and maintain its trajectory. This is why planes are designed to have a specific weight and size to ensure optimal flight performance.

## 5. What tools or equations are used to calculate the trajectory of a plane?

To calculate the trajectory of a plane, scientists and engineers use equations such as Newton's laws of motion and Bernoulli's principle. In addition, advanced computer simulations and models are used to accurately predict the trajectory of a plane under various conditions.

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